TSTP Solution File: SEU161+3 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU161+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:53 EDT 2022
% Result : Theorem 0.16s 0.34s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 11 ( 2 unt; 3 typ; 0 def)
% Number of atoms : 22 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 22 ( 9 ~; 5 |; 0 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 18 ( 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(set_union2_type,type,
set_union2: ( $i * $i ) > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(1,plain,
^ [A: $i,B: $i] :
rewrite(
( ( in(A,B)
=> ( set_union2(singleton(A),B) = B ) )
<=> ( ~ in(A,B)
| ( set_union2(singleton(A),B) = B ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i,B: $i] :
( in(A,B)
=> ( set_union2(singleton(A),B) = B ) )
<=> ! [A: $i,B: $i] :
( ~ in(A,B)
| ( set_union2(singleton(A),B) = B ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,axiom,
! [A: $i,B: $i] :
( in(A,B)
=> ( set_union2(singleton(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
tff(4,plain,
! [A: $i,B: $i] :
( ~ in(A,B)
| ( set_union2(singleton(A),B) = B ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ~ ! [A: $i,B: $i] :
( in(A,B)
=> ( set_union2(singleton(A),B) = B ) )
<=> ~ ! [A: $i,B: $i] :
( ~ in(A,B)
| ( set_union2(singleton(A),B) = B ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ ! [A: $i,B: $i] :
( in(A,B)
=> ( set_union2(singleton(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
tff(7,plain,
~ ! [A: $i,B: $i] :
( ~ in(A,B)
| ( set_union2(singleton(A),B) = B ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU161+3 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Sep 3 09:44:28 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.34 % SZS status Theorem
% 0.16/0.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------